Interaction phenomena between a lump and other multi-solitons for the $${\mathbf {(2+1)}}$$ ( 2 + 1 ) -dimensional BLMP and Ito equations

Abstract

In this paper, “new” interaction solutions between a lump solution and other multi-soliton (kinky or stripe) solutions are studied through developing a “new” direct method based on the Hirota bilinear form for the $$(2+1)$$ -dimensional BLMP equation and the $$(2+1)$$ -dimensional Ito equation. Interaction solutions degenerate into lump (or kinky/stripe) solutions while the involved exponential function (or quadratic function) disappears. The interaction phenomena in the presented solutions show that a lump can be drowned or swallowed by other multi-solitary waves (kinky or stripe waves), and such interactions are very rare non-elastic collisions. What is more, we find that the positions of the interaction between a lump and three or four kinky waves are different while we choose different parameters, and the collisions may be at the bottom, middle, top or other positions. The dynamic characteristics of the constructed interaction solutions are illustrated by sequences of interesting figures plotted with the help of Maple.